1. Field of the Invention
This invention relates to a method for compressing an image signal. This invention particularly relates to a method for compressing an image signal, wherein wavelet transformation is utilized and a high signal compressibility is thereby obtained. This invention also relates to a method for reconstructing an image signal, wherein an original image signal is reconstructed from an image signal having been compressed with the method for compressing an image signal in accordance with the present invention.
2. Description of the Prior Art
Image signals representing continuous tone images, such as television signals, are composed of enormous amounts of information, and a broad-band transmission line is required for transmission of the image signals. Such image signals involve much redundancy, and various attempts have been made to compress the image signals by restricting the redundancy. Also, in recent years, recording of continuous tone images on optical disks, magnetic disks, or the like, has been generally put into practice. In such cases, image signal compression is generally carried out for the purpose of efficiently recording the image signals on a recording medium.
As one of the methods for compressing an image signal, a compressing processing method utilizing prediction encoding has heretofore been employed. Specifically, in cases where an image signal is to be stored or transmitted, the image signal is subjected to compression processing based on prediction encoding, and the amount of the image signal is thereby reduced. The compressed image signal is then stored or transmitted. When the image which is represented by the image signal is to be reproduced, the compressed image signal is subjected to decoding processing and is thereby decompressed. Thereafter, a visible image is reproduced from the decompressed image signal.
Also, as one of the methods for compressing an image signal, a method utilizing vector quantization has heretofore been used. The method comprises the steps of (i) dividing a two-dimensional image signal into blocks, each of which comprises the image signal components representing K number of picture elements adjacent to one another in the image, (ii) selecting a vector, which corresponds with the minimum distortion to the set of the image signal components in each of the blocks, from a code book composed of a plurality of vectors, which are different from one another and prepared in advance by defining K number of vector elements, and (iii) encoding the information, which represents the selected vector, in association with the block.
Since the image signal components in the block as described above have high correlation to one another, the image signal components in each block can be represented very accurately by one of a comparatively small number of vectors prepared in advance. Therefore, instead of the actual image signal being transmitted or recorded, transmission or recording of the image signal can be carried out by transmitting or recording the codes representing the vectors. In this manner, signal compression can be achieved. By way of example, the amount of the image signal components, which represent 64 picture elements in a continuous tone image having 256 levels (=8 bits) of density scale, is 8.times.64=512 bits. In such cases, the image signal components representing the 64 picture elements may be grouped as a single block, and the image signal components in the block may be represented by a vector, which is composed of 64 vector elements. Also, a code book including 256 such vectors may be prepared. In such cases, the amount of the information per block becomes equal to the amount of the information required to discriminate between the vectors, i.e. 8 bits. Consequently, in such cases, the amount of the signal can be compressed to 8/(8.times.64)=1/64.
The image signal is compressed in the manner described above, and the compressed image signal is recorded or transmitted. Thereafter, the vector elements of each of the vectors, which are represented by the vector discriminating information, are taken as reconstructing information for each of the blocks, and the original image is reproduced by using the reconstructing information.
One approach to improvement of the compressibility in the image signal compression by prediction encoding is to decrease the bit resolution (density resolution) of the image signal, i.e. to carry out quantization processing for quantizing the image signal more coarsely, in addition to prediction encoding processing.
Therefore, in U.S. Pat. No. 4,776,029, the applicant proposed a method for compressing an image signal with interpolation encoding, wherein the prediction encoding technique and the quantization technique are combined with each other. With the proposed method, image signal components of an image signal are classified into main components, which have been sampled at appropriate sampling intervals, and interpolated components other than the main components. The interpolated components are then subjected to interpolation prediction encoding processing based on the main components, i.e. the values of the interpolated components are predicted with the interpolation prediction from the main components. Thereafter, prediction errors between the predicted values and the actual values of the interpolated components are encoded into variable length codes, such as Huffman codes (i.e. are converted into codes, the lengths of which vary for different values of the prediction errors). In this manner, the image signal is compressed.
During the compression of an image signal, the image signal compressibility should be as high as possible. However, it is technically difficult to increase the compressibility markedly during the interpolation encoding. Therefore, in order for a high compressibility to be achieved, it is considered that component number decreasing processing, which results in a coarse spatial resolution, and the interpolation encoding be combined with each other.
Therefore, in U.S. Pat. No. 5,086,489, the applicant proposed a method for compressing an image signal, wherein the interpolation encoding and the component number decreasing processing are combined with each other, and wherein a high compressibility is achieved while good image quality is being kept.
As a method for processing an image signal, the so-called "wavelet transformation method" has heretofore been proposed.
How the wavelet transformation is carried out will be described hereinbelow.
The wavelet transformation has recently been developed as a frequency analysis method and has heretofore been applied to stereo pattern matching, signal compression, and the like. The wavelet transformation is described in, for example, "Wavelets and Signal Processing," by Olivier Rioul and Martin Vetterli, IEEE SP Magazine, pp. 14-38, October 1991; and "Zero-Crossings of a Wavelet Transform," by Stephane Mallat, IEEE Transactions on Information Theory, Vol. 37, No. 4, pp. 1019-1033, July 1991.
With the wavelet transformation, a signal is transformed into frequency signals, each being of one of a plurality of different frequency bands, by utilizing a function h, which is shown in FIG. 7, as a basic function and in accordance with the formula ##EQU1## wherein f(t): the signal having an arbitrary wave form,
W(a,b); the wavelet transformation of f(t), ##EQU2## a: the degree of contraction of the function, b: the amount of movement in the horizontal axis direction. PA1 i) carrying out wavelet transformation on the original image signal, the original image signal being thereby decomposed into image signals, each being of one of a plurality of different frequency bands, PA1 ii) determining the degree of importance of each of different portions of the image from one of the image signals or from the original image signal, PA1 iii) carrying out labeling processing on the image signal, from which the degree of importance of each of different portions of the image was determined, in accordance with the determined degree of importance of each of different portions of the image, PA1 iv) quantizing the image signals in accordance with the results of the labeling processing such that a larger number of bits may be allocated to each of picture elements in a portion of the image determined as having a higher degree of importance, and PA1 v) encoding the image signals, which have thus been quantized. PA1 i) decoding the image signals, which have been encoded with a method for compressing an image signal in accordance with the present invention, and PA1 ii) carrying out inverse wavelet transformation on the image signals, which have thus been decoded.
Therefore, the problems with regard to a false oscillation, which occurs with Fourier transformation, do not occur. Specifically, when filtering processing is carried out by changing the period and the degree of contraction of the function h and moving the function h on an original signal, frequency signals, each of which is adapted to one of desired frequencies ranging from a fine frequency to a coarse frequency. By way of example, FIG. 8 shows signals, which are obtained by carrying out the wavelet transformation on an original signal Sorg and then carrying out inverse wavelet transformation for each of frequency bands. FIG. 9 shows signals, which are obtained by carrying out Fourier transformation on the original signal Sorg and then carrying out inverse Fourier transformation for each of the frequency bands. As will be understood from FIGS. 8 and 9, the wavelet transformation has the advantage over the Fourier transformation in that a frequency signal of a frequency band corresponding to the oscillation of the original signal Sorg can be obtained. Specifically, with the Fourier transformation, an oscillation occurs in a part B' of a frequency band 7, which corresponds to a part B of the original signal Sorg. However, with the wavelet transformation, as in the original signal Sorg, no oscillation occurs in a part A' of a frequency band W7, which corresponds to a part A of the original signal Sorg.
Also, a method for compressing an image signal by utilizing the wavelet transformation has been proposed in, for example, "Image Coding Using Wavelet Transform" by Marc Antonini, et al., IEEE Transactions on Image Processing, Vol. 1, No. 2, pp. 205-220, April 1992.
With the proposed method, wavelet transformation is carried out on an original image signal representing an image, and the original image signal is thereby transformed into image signals, each being of one of a plurality of different frequency bands. Thereafter, vector quantization is carried out on each of the image signals such that a small number of bits per picture element may be allocated to an image signal of a high frequency band, which image signal carries much noise, and a large number of bits per picture element may be allocated to an image signal of a low frequency band, which image signal carries the information representing the major object. In this manner, the original image signal is compressed. With the proposed method, the compressibility of the original image signal can be kept high. Also, the original image can be restored perfectly by carrying out inverse wavelet transformation on the compressed image signal.
However, with the aforesaid method for compressing an image signal by utilizing the wavelet transformation, it is necessary for the image signal to be compressed by vector quantization. Therefore, if the compressibility is increased even further, there will be the risk that the image quality of the original image is lost. Thus there is a limit in the increase in the compressibility of the image signal.